Lectures on Symplectic Geometry by Ana Cannas da Silva
Lectures on Symplectic Geometry - Table of Contents
- PART I: SYMPLECTIC MANIFOLDS
- 1. Symplectic Forms and Linear Algebra
- 2. Symplectic Form on the Cotangent Bundle
- PART II: SYMPLECTOMORPHISMS
- 3. Lagrangian Submanifolds
- 4. Generating Functions
- 5. Poincaré Recurrence Theorem
- PART III: LOCAL FORMS
- 6. Preparation for Local Theory
- 7. Moser Theorems
- 8. Darboux–Moser–Weinstein Theory
- 9. Weinstein Tubular Neighborhood Theorem
- PART IV: CONTACT MANIFOLDS
- 10. Contact Forms and Distribution
- 11. Contact Dynamics and Reeb Vector Fields
- PART V: COMPATIBLE ALMOST COMPLEX STRUCTURES
- 12. Almost Complex Structures
- 13. Compatible Triples
- 14. Dolbeault Theory
- PART VI: KÄHLER MANIFOLDS
- 15. Complex Manifolds
- 16. Kähler Forms and Metrics
- 17. Compact Kähler Manifolds
- PART VII: HAMILTONIAN MECHANICS
- 18. Hamiltonian Vector Fields
- 19. Variational Principles
- 20. Legendre Transform
- PART VIII: MOMENT MAPS
- 21. Lie Group Actions
- 22. Hamiltonian Actions
- PART IX: SYMPLECTIC REDUCTION
- 23. The Marsden–Weinstein–Meyer Theorem
- 24. Symplectic Reduction Technique
- PART X: MOMENT MAPS REVISITED
- 25. Moment Map in Gauge Theory
- 26. Existence and Uniqueness of Moment Maps
- 27. Convexity Properties
- PART XI: SYMPLECTIC TORIC MANIFOLDS
- 28. Classification of Symplectic Toric Manifolds
- 29. Delzant Construction
- 30. Duistermaat–Heckman Theorems
What You Will Learn in Lectures on Symplectic Geometry
Lectures on Symplectic Geometry by Ana Cannas da Silva offers an elegant and accessible entry point into modern symplectic topology and geometric mechanics. Accessing this cannas da silva symplectic geometry pdf enables mathematicians, topologists, and theoretical physicists to explore Darboux's theorem, cotangent bundles, and contact structures.
The volume comprehensively covers Poisson brackets, Lie group actions, symplectic reduction, momentum maps, and Delzant's theorem on toric manifolds. Studying this indispensable lectures on symplectic geometry book equips graduate students with vital tools for research in geometric quantization and Hamiltonian dynamics.
Available as an open academic download lectures on symplectic geometry pdf download, this classic reference remains a gold standard textbook for advanced courses in differential geometry and topology.
Book Details & Specifications
Title:
Lectures on Symplectic Geometry by Ana Cannas da Silva
Publisher:
Springer
Year:
2006
Pages:
225
Type:
PDF
Language:
English
ISBN-10 #:
3540421955
ISBN-13 #:
978-3540421955
License:
External Educational Resource
Amazon:
Amazon
About the Author: Ana Cannas da Silva
The author Ana Cannas da Silva
is a distinguished Portuguese mathematician and Senior Scientist at ETH Zürich, recognized globally for her expertise in symplectic geometry, geometric topology, and toric manifolds.
Renowned for her exceptional pedagogical clarity, her textbook Lectures on Symplectic Geometry by Ana Cannas da Silva is widely adopted in graduate mathematics programs around the world.
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